um i dont remember much but i'l try
3cos^2x= 2sinx+2
3(1-sin^2x)=2sinx+2
3-3sin^2x=2sinx+2
0= 3sin^2x + 2sinx-1
(3sinx-1)(sinx +1)
sinx=1/3 and sinx=-1
and find the sin values between the limits from there

(Original post by matt^)
OP - may i ask why someone is doing C2 work in the middle of the summer though?

I don't think doing some sort of work over the summer, how much or how little it may be, is particularly uncommon (especially for a TSR user ). People have plenty of reasons. Personally, I'm doing a little work out of interest (well, mostly out of interest - I can't honestly say that FP2 differential equations are that exciting).